Using Partial Products to Multiply Whole Numbers 5.NBT.B.5.
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Using Partial Products to Multiply Whole Numbers 5.NBT.B.5
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Transcript of Using Partial Products to Multiply Whole Numbers 5.NBT.B.5.
Using Partial Products to Multiply Whole Numbers
5.NBT.B.5
Multiplying two numbers that are each greater than 10 requires some new strategies.Let’s begin by looking at a picture that shows 18 x 13.
1183×
Using Partial Products to Multiply Whole Numbers
3
100
13
10 18 8
10
234
To show 18 x 13, here is a large array of squares.This array measures 18 squares …… by 13 squares.18 is equal to …10 + 813 is equal to …10 + 3What is 10 x 10?100What is 8 x 10?80What is 10 x 3?30What is 8 x 3?24What is the sum of 100 + 80 + 30 + 24?234To find the total number of squares, we can multiply 18 by 13.We can also decompose 18 and 13 into smaller numbers, and then multiply those numbers.Now, let’s multiply the parts of the picture. Then we can add those parts together.
803024
So, 234 is the product of 18 and 13.
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Using Partial Products to Multiply Whole Numbers
18 13
234
18 × 13 = 234
13 × 18 = 234
234 ÷ 18 = 13
234 ÷ 13 = 18
Since we know that 18 x 13 …… is equal to 234 …… we also know that 13 x 18 …… is equal to 234.We also know that 234 divided by 18 …… is equal to 13.And, 234 divided by 13 …… is equal to 18.
Using Partial Products to Multiply Whole Numbers
1175×
Here is 17 x 15. Let’s look at a picture that shows 17 x 15.
Using Partial Products to Multiply Whole Numbers
5
100
15
10 17 7
10
255
To show 17 x 15, here is a large array of squares.… by 15 squares.17 is equal to …10 + 715 is equal to …10 + 5What is 10 x 10?100What is 7 x 10?70What is 10 x 5?50What is 7 x 5?35What is the sum of 100 + 70 + 50 + 35?255
705035
So, 255 is the product of 17 and 15.This array measures 17 squares …To find the total number of squares, we can multiply 17 by 15.We can also decompose 17 and 15 into smaller numbers, and then multiply those numbers.Now, let’s multiply the parts of the picture. Then we can add those parts together.
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Using Partial Products to Multiply Whole Numbers
17 15
255
17 × 15 = 255
15 × 17 = 255
255 ÷ 17 = 15
255 ÷ 15 = 17
Since we know that 17 x 15 …… is equal to 255 …… we also know that 15 x 17 …… is equal to 255.255 divided by 17 …… is equal to 15.And, 255 divided by 15 …… is equal to 17.
Using Partial Products to Multiply Whole Numbers
Here is 19 x 14. Let’s look at a picture that shows 19 x 14.
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Using Partial Products to Multiply Whole Numbers
4
100
14
10 19 9
10
266
To show 19 x 14, here is a large array of squares.… by 14 squares.19 is equal to …10 + 914 is equal to …10 + 4What is 10 x 10?100What is 9 x 10?90What is 10 x 4?40What is 9 x 4?36What is the sum of 100 + 90 + 40 + 36?266
904036
So, 266 is the product of 19 and 14.This array measures 19 squares …To find the total number of squares, we can multiply 19 by 14.We can also decompose 19 and 14 into smaller numbers, and then multiply those numbers.Now, let’s multiply the parts of the picture. Then we can add those parts together.
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Using Partial Products to Multiply Whole Numbers
19 14
266
19 × 14 = 266
14 × 19 = 266
266 ÷ 19 = 14
266 ÷ 14 = 19
Since we know that 19 x 14 …… is equal to 266 …… we also know that 14 x 19 …… is equal to 266.266 divided by 19 …… is equal to 14.And, 266 divided by 14 …… is equal to 19.
Using Partial Products to Multiply Whole Numbers
Here is 38 x 23.
238
3×
Using Partial Products to Multiply Whole Numbers
3
600
23
3038 8
20
874
To show 38 x 23, here is a sketch.… by 23.38 is equal to …30 + 823 is equal to …20 + 3What is 30 x 20?600What is 8 x 20 ?160What is 30 x 3?90What is 8 x 3?24What is the sum of 600 + 160 + 90 + 24?874
1609024
So, 874 is the product of 38 and 23.This shows 38 …On the sketch, let’s draw two lines …… so that we can decompose each number.Now, let’s multiply the parts of the picture. Then we can add those parts together.
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Using Partial Products to Multiply Whole Numbers
38 23
874
38 × 23 = 874
23 × 38 = 874
874 ÷ 38 = 23
874 ÷ 23 = 38
Since we know that 38 x 23 …… is equal to 874 …… we also know that 23 x 38 …… is equal to 874.874 divided by 38 …… is equal to 23.And, 874 divided by 23 …… is equal to 38.
Using Partial Products to Multiply Whole Numbers
Here is 56 x 82.
856
2×
Using Partial Products to Multiply Whole Numbers
2
4,000
82
5056 6
80
4,592
To show 56 x 82, here is a sketch.… by 82.56 is equal to …50 + 682 is equal to …80 + 2What is 50 x 80?4,000What is 6 x 80?480What is 50 x 2?100What is 6 x 2?12What is the sum of 4,000 + 480 + 100 + 12?4,592
480100
12
So, 4,592 is the product of 56 and 82.This shows 56 …On the sketch, let’s draw two lines …… so that we can decompose each number.Now, let’s multiply the parts of the picture. Then we can add those parts together.
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Using Partial Products to Multiply Whole Numbers
Closing Question
Using Partial Products to Multiply Whole Numbers
Here is 75 x 64.
675
4×
Using Partial Products to Multiply Whole Numbers
4
4,200
64
7075 5
60
4,800
To show 75 x 64, here is a sketch.… by 64.75 is equal to …70 + 564 is equal to …60 + 4What is 70 x 60?4,200What is 5 x 60?300What is 70 x 4?280What is 5 x 4?20What is the sum of 4,200 + 300 + 280 + 20?4,800
300280
20
So, 4,800 is the product of 75 and 64.This shows 75 …On the sketch, let’s draw two lines …… so that we can decompose each number.Now, let’s multiply the parts of the picture. Then we can add those parts together.
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Using Partial Products to Multiply Whole Numbers
